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United States Patent Application 
20170131242

Kind Code

A1

KANNAJOSYULA; Haraprasad
; et al.

May 11, 2017

BEAM FORMING AND STEERING OF HELICAL GUIDED WAVES IN PIPELIKE AND
PLATELIKE STRUCTURES
Abstract
A method of inspecting a pipe for flaws includes emitting ultrasonic
waves, controlling the emission of the ultrasonic waves, receiving
reflections of the ultrasonic waves, and determining at least one
characteristic of one or more flaws. The ultrasonic waves are emitted in
a helical pattern through the pipe from an array of ultrasonic transducer
elements. The emission of the ultrasonic waves from the array is
controlled such that the ultrasonic waves are emitted at a plurality of
helical angles within a range of helical angles. The reflections of the
ultrasonic waves are caused by impingement of the ultrasonic waves on the
one or more flaws. The at least one characteristic of the one or more
flaws is determined based on the received reflections of the ultrasonic
waves.
Inventors: 
KANNAJOSYULA; Haraprasad; (Seattle, WA)
; NINO; Giovanni; (Issaquah, WA)
; BONDURANT; Phillip D.; (Covington, WA)
; FRATELLO; Vincent; (Bellevue, WA)

Applicant:  Name  City  State  Country  Type  QI2 Elements, LLC  Kent  WA  US 
 
Assignee: 
QI2 Elements, LLC
Kent
WA

Family ID:

1000002420228

Appl. No.:

15/322064

Filed:

June 24, 2015 
PCT Filed:

June 24, 2015 
PCT NO:

PCT/US2015/037376 
371 Date:

December 23, 2016 
Related U.S. Patent Documents
      
 Application Number  Filing Date  Patent Number 

 62016569  Jun 24, 2014  

Current U.S. Class: 
1/1 
Current CPC Class: 
G01N 29/262 20130101; G01N 29/04 20130101; G01N 2291/2634 20130101; G01N 2291/044 20130101; G01N 2291/106 20130101 
International Class: 
G01N 29/26 20060101 G01N029/26; G01N 29/04 20060101 G01N029/04 
Claims
1. A method of inspecting a pipe for flaws comprising: emitting
ultrasonic waves in a helical pattern through the pipe from an array of
ultrasonic transducer elements; controlling the emission of the
ultrasonic waves from the array such that the ultrasonic waves are
emitted at a plurality of helical angles within a range of helical
angles; receiving reflections of the ultrasonic waves, the reflections of
the ultrasonic waves caused by impingement of the ultrasonic waves on one
or more flaws; and determining at least one characteristic of the one or
more flaws based on the received reflections of the ultrasonic waves.
2. The method of claim 1, wherein the at least one characteristic of the
one or more flaws comprises one or more of a location of the one or more
flaws, a size of the one or more flaws, an orientation of the one or more
flaws, or a shape of the one or more flaws.
3. The method of claim 1, wherein the at least one characteristic of the
one or more flaws is determined based a presence or an absence of an
anomalous signature, the method further comprising: mapping the at least
one characteristic based on at least one of an amplitude distribution in
time, an amplitude distribution in frequency, arrival time, or direction
of approach of the anomalous signature.
4. A device for inspecting a structure for flaws, the device comprising:
at least one ultrasonic emitter configured to emit waves in the
structure; at least one ultrasonic receiver configured to receive
reflections of the waves caused by impingement of the waves on one or
more flaws; and a computing system configured to: control emission of
waves from the at least one ultrasonic transducer in helical patterns
based on one or more control parameters, the one or more control
parameters comprising at least a windowed pulsed signal comprising at
least a half oscillation of any shape; and determine at least one
characteristic of one or more flaws in the structure based on the signals
emitted from the array and the reflections of the waves received by the
array.
5. The device of claim 4, wherein the one or more control parameters
further comprise at least one of: a continuous oscillation of signal
amplitudes; a variance of signal frequency over time; a prescribed range
of frequencies; or a variance of one or more of time delays, amplitudes,
number cycles, pulse lengths, or frequencies.
6. The device of claim 4, wherein further comprising: an array comprising
the at least one ultrasonic emitter and the at least one ultrasonic
receiver.
7. The device of claim 5, further comprising: at least one additional
ultrasonic receiver configured to receive one or more of the waves
emitted by the array or the reflections of the waves, wherein the at
least one additional ultrasonic receiver is separate from the array;
wherein the computing system is further configured to determine the at
least one characteristic of the one or more flaws based on the
characteristics of reflected or transmission of waves received by the at
least one additional ultrasonic receiver.
8. The device of claim 4, wherein the computing system is configured to
evaluate and select one or more of a guided wave subtype of the waves,
helical paths of the waves, or a focal point of the waves.
9. The device of claim 4, wherein the structure is a pipe.
10. The device of claim 9, wherein the pipe comprises at least one of a
circular crosssection, a square crosssection, a triangular
crosssection, any other polygonal crosssection, or a crosssection that
rotates along an axis of the pipe.
11. The device of claim 9, wherein at least one emitter is configured to
emit omnidirectional waves, wherein at least one ultrasonic transducer
element comprises the at least one ultrasonic emitter and the at least
one ultrasonic receiver, and wherein the at least one ultrasonic
transducer element is in a configuration determined by a direction of
oscillation relative to waves propagating in the pipe or to an axis of
the pipe.
12. The device of claim 11, wherein the oscillation is along a thickness
of the pipe, and wherein the at least one ultrasonic transducer element
is a thickness mode piezoelectric transducer or a particularlyshaped 13
piezocomposite transducer.
13. The device of claim 11, wherein the oscillation is along the axis of
the pipe, and wherein the at least one ultrasonic transducer element is a
circularshaped macrofiber composite with piezoelectric fibers oriented
perpendicular to the axis and comprises electrodes arranged along the
axis of the pipe.
14. The device of claim 11, wherein the oscillation is tangential and
orthogonal to the axis of the pipe, and wherein the at least one
ultrasonic transducer element is a circularshaped macrofiber composite
with piezoelectric fibers oriented perpendicular to the axis and
comprises electrodes arranged perpendicular to the axis of the pipe.
15. The device of claim 11, wherein the oscillation is tangential and
orthogonal to the waves, and wherein the at least one ultrasonic
transducer element is a circularshaped macrofiber composite with
piezoelectric fibers forming an annular array and comprises electrodes
oriented radially from the center of the annular array.
16. The device of claim 11, wherein the oscillation is tangential and
parallel to the waves, and wherein the at least one ultrasonic transducer
element comprises electrodes forming an annular array, and wherein the at
least one ultrasonic transducer element is a circularshaped macrofiber
composite with piezoelectric fibers oriented radially from the center of
the annular array.
17. The device of claim 4, wherein the at least one ultrasonic emitter is
configured to emit waves both unidirectionally and bidirectionally.
18. The device of claim 4, wherein the structure comprises a plate like
structure.
19. The device of claim 4, wherein the computing system is further
configured to determine at least one characteristic of one or more flaws
in the structure based at least in part on the following formula: .PHI.
= .phi..XI. .alpha. [ .PSI. r .PSI. .theta.
.PSI. z ] = [ .psi. T 1 .psi. T 2 0
 .psi. T 2 .psi. T 1 0 0 0 .psi.
z ] [ .differential. .XI. .beta. / .differential. r
1 r .differential. .XI. .beta. .differential. .theta.
.XI. .beta. ] ##EQU00027## wherein .PHI. is a Helmholtz scalar
potential; wherein .PSI..sub.r, .PSI..sub..theta. and .PSI..sub.z are
components of a Helmholtz vector potential; wherein .phi., .psi..sub.Tj;
j=1,2 and .psi..sub.z are arbitrary constants; and wherein
.XI..sub..eta., .eta.=.alpha.,.beta. is a function of the form exp
i(.eta.r cos(.theta..theta..sub..eta.)+k.sub.zz.omega.t).
20. The device of claim 4, wherein the computing system is further
configured to determine at least one characteristic of one or more flaws
in the structure based at least in part a time delay supplemented by
amplitude control based on a minimum time delay increment, and wherein
the minimum time delay is a characteristic of hardware in the device.
21. The method of claim 1, further comprising: controlling one or more of
an average value of the range of helical angles or a width of the range
of helical angles.
22. The device of claim 9, wherein the pipe is a bent pipe.
23. The device of claim 4, wherein the computing system is configured to
process received data from independent actuation of transducer array
elements to mimic effects of real beam forming.
Description
CROSSREFERENCE(S) TO RELATED APPLICATION(S)
[0001] This application claims the benefit of U.S. Provisional Application
No. 62/016,569, filed Jun. 24, 2014, the contents of which are
incorporated herein by reference in their entirety.
BACKGROUND
[0002] Traditional methods employing guided waves for inspecting pipes
comprise two stages. The first stage is illustrated in FIG. 1 where a
pipe section 20 has an array of transducers 22 mounted over the
circumference and an axially propagating guided wave 24. In the first
stage, an axially propagating, unfocussed, guided wave is generated by
exciting the transducers in the array of transducers 22 simultaneously so
that the energy of the wave packet is distributed around the
circumference of pipe. This method is limited to detecting flaws that can
be attributed to material loss or flaws with circumferential extent (see
Hardie F., "Evaluation of the effectiveness of nondestructive testing
screening methods for inservice inspection," Report for the Health and
Security Officer, UK, 2009, pages 2930).
[0003] For the first stage, the disadvantage of traditional methods is
that the flaws must necessarily be either material loss type or
circumferentially oriented because of the direction of wave propagation.
Because the energy of the wave is distributed throughout the
circumference, the intensity of the wave is low leading to its premature
dissipation when pipe is carrying fluid or is submerged or buried (see
Hardie F, "Evaluation of the effectiveness of nondestructive testing
screening methods for inservice inspection," Report for the Health and
Security Officer, UK, 2009, pages 2930).
[0004] The second stage can overcome the limitations of the first stage by
providing high intensity ultrasound at the region of interest. The second
stage is illustrated in FIG. 2 where a pipe section 26 has an array of
transducers 28 mounted over the circumference. A focused waveguide 30
that focuses rays 32 emitted from the array of transducers 28 just before
the focal point. One of the disadvantages of the focusing method, when
compared to the unfocused guided wave method, is that the inspection is
pointbypoint which, can be time consuming. The time required for
capture can be on the order of 1 ms or more per point for the best case
scenario (see, e.g., Li, J. et al "Angularprofile tuning of guided waves
in hollow cylinders using a circumferential phased array," Ultrasonics,
Ferroelectrics and Frequency Control, IEEE Transactions on 49.12, 2002,
pages 17201729; see also, e.g., Sun, Z. et al., "Flexural torsional
guided wave mechanics and focusing in pipe," Journal of pressure vessel
technology 127.4, 2005, pages 471478).
[0005] Focusing is typically achieved by actuating the array of sensors
with time delayed signals through a system, such as the embodiment of a
system depicted in FIG. 3. The system includes an ultrasonic transducer
array 34 mounted on a pipe, a multichannel preamplifier 36 that receives
rays emitted by the ultrasonic transducer array 34, a multichannel analog
to digital converter 38, and a computer/controller 40. The system also
includes a pulse generator 42 controlled by the computer/controller 40
with variable time delays, amplitudes, frequencies and cycles across the
channels. Control signals are sent from the pulse generator 42 to the
ultrasonic transducer array 34 to control the emission of rays from the
ultrasonic transducer array 34. The system also optionally includes an
ultrasonic receiver array 44 mounted on the pipe.
[0006] Other disadvantages of the focusing method relate to factors
involving the hardware depicted in FIG. 3, such as latency of the
hardware when settings are changed to shift the point of focus. The
circumferential location of the focal point is changed by switching the
order in which the transducer array elements are excited (see Sun, Z. et
al., "Flexural torsional guided wave mechanics and focusing in pipe,"
Journal of pressure vessel technology 127.4, 2005, pages 1724 and 1727).
Another disadvantage to the guided wave focusing method is the limited a
circumferential resolution based on the number of elements in the array.
Another disadvantage of the traditional focusing method that can be
deduced from literature is that it is most sensitive to flaws that have a
circumferential extent because the focused beam is formed by symmetric
contribution from all the transducers, as illustrated by the rays 32
depicted in FIG. 2.
[0007] The second stage is typically used to size and find the
circumferential location of the flaw. Focused guided waves can also be
optionally used to generate a Cscan or a detailed map of a pipe by
inspecting it pointbypoint as the focal point of the wave axially and
circumferentially shifted by manipulating the transducer elements'
excitation.
[0008] All of the above methods are ineffective when there are two flaws
with one flaw hidden behind the shadow of another, as illustrated in FIG.
4. In FIG. 4, a pipe 46 includes a transducer array 48 that produce
incident rays 50 corresponding to the focused guided wave generated by
the transducer array 48 in the pipe 46. The pipe includes a first flaw 54
and a second flaw 56. The first flaw 54 is bigger than the second flaw 56
and the second flaw is located in a shadow of the first flaw 54. The
incident rays 50 are reflected by the first flaw 54 and reflection rays
52 return away from the first flaw 54. The first flaw 54 is larger than
the second flaw 56 and the second flaw 56 is located in a shadow of the
first flaw 54. As a result, as shown in FIG. 4, the incident rays 50 and
the reflection rays 52 not hit the second flaw 56 and the second flaw 56
cannot be detected.
[0009] Mixing of the ultrasound array parameters, namely, time delays and
amplitude variation is known as apodization. Apodization has been
suggested in literature as a method for improving spot size of the
focused waves. The primary aim of apodization thus far has been to reduce
the so called Fourier noise caused due to the finite geometrical extent
of an array of transducers. Further, apodization is performed without
taking into account the fact that the minimum time delay offered by
hardware limits the frequency at which good quality beam forming is
achieved. Recently, it was shown that time delays can be completely
replaced by amplitude variation across the transducer elements (see
Kannajosyula, H., et al., "Amplitude controlled array transducers for
mode selection and beam steering of guided waves in plates," Review of
Progress in Quantitative Nondestructive Evaluation: Volume 32, American
Institute of Physics, 2013). By virtue of the principle of reciprocity,
theories developed for beam steering have enabled the development of
postprocessing algorithms in literature for tools that employ an array
of ultrasonic sensors each of which discretely transmit and/or receive
ultrasonic guided wave signals in the structure. Such postprocessing
algorithms are able to filter flaw signatures from the received data and
thereby image the structure. Such algorithms are commonly referred to as
synthetic phased array method and tools employing such algorithms have
been referred to as ultrasonic radar or ultrasonic guided wave radar.
[0010] Unfocused beam forming in plates has been shown to be possible
(see, e.g., Kannajosyula, H., et al., "Amplitude controlled array
transducers for mode selection and beam steering of guided waves in
plates," Review of Progress in Quantitative Nondestructive Evaluation:
Volume 32, American Institute of Physics. 2013). In principle, wave
propagation in a pipe of very large diameter and small wall thickness
will be similar to that in a plate. However, this may not necessarily be
true for pipes of smaller diameters. Hence extension of beam forming
technique used in plates to beam forming in pipes is not straightforward.
Conversely, a method for focused beam forming in plates has not yet been
developed in literature. Theory used for pipes can be extended to plates
by modeling plates as very large diameter pipes. However; current theory
appears to need further development for this to be possible.
SUMMARY
[0011] This summary is provided to introduce a selection of concepts in a
simplified form that are further described below in the Detailed
Description. This summary is not intended to identify key features of the
claimed subject matter, nor is it intended to be used as an aid in
determining the scope of the claimed subject matter.
[0012] In one embodiment, a method of inspecting a pipe for flaws includes
emitting ultrasonic waves, controlling the emission of the ultrasonic
waves, receiving reflections of the ultrasonic waves, and determining at
least one characteristic of one or more flaws. The ultrasonic waves are
emitted in a helical pattern through the pipe from an array of ultrasonic
transducer elements. The emission of the ultrasonic waves from the array
is controlled such that the ultrasonic waves are emitted at a plurality
of helical angles within a range of helical angles. The reflections of
the ultrasonic waves are caused by impingement of the ultrasonic waves on
the one or more flaws. The at least one characteristic of the one or more
flaws is determined based on the received reflections of the ultrasonic
waves.
[0013] In one example, the at least one characteristic of the one or more
flaws includes one or more of a location of the one or more flaws, a size
of the one or more flaws, an orientation of the one or more flaws, or a
shape of the one or more flaws. In another example, the at least one
characteristic of the one or more flaws is determined based on a presence
or an absence of an anomalous signature. In another example, the method
further includes mapping the at least one characteristic based on at
least one of an amplitude distribution in time, an amplitude distribution
in frequency, arrival time, or direction of approach of the anomalous
signature. In another example, the method further includes controlling
one or more of an average value of the range of helical angles or a width
of the range of helical angles.
[0014] In another embodiment, a device for inspecting a structure for
flaws includes at least one ultrasonic emitter configured to emit waves
in the structure, at least one ultrasonic receiver configured to receive
reflections of the waves caused by impingement of the waves on one or
more flaws, and a computing system. The a computing system is configured
to control emission of waves from the at least one ultrasonic transducer
in helical patterns based on one or more control parameters and determine
at least one characteristic of one or more flaws in the structure based
on the signals emitted from the array and the reflections of the waves
received by the array. The one or more control parameters includes at
least a windowed pulsed signal comprising at least a half oscillation of
any shape.
[0015] In one example, the one or more control parameters further includes
at least one of: a continuous oscillation of signal amplitudes, a
variance of signal frequency over time, a prescribed range of
frequencies, or a variance of one or more of time delays, amplitudes,
number cycles, pulse lengths, or frequencies. In another example, the
device further includes an array comprising the at least one ultrasonic
emitter and the at least one ultrasonic receiver. In another example, the
device further includes at least one additional ultrasonic receiver
configured to receive one or more of the waves emitted by the array or
the reflections of the waves, where the at least one additional
ultrasonic receiver is separate from the array. In another example, the
computing system is further configured to determine the at least one
characteristic of the one or more flaws based on the characteristics of
reflected or transmission of waves received by the at least one
additional ultrasonic receiver. In yet another example, the computing
system is configured to evaluate and select one or more of a guided wave
subtype of the waves, helical paths of the waves, or a focal point of the
waves.
[0016] In another example, the structure is a pipe. In another example,
the pipe comprises at least one of a circular crosssection, a square
crosssection, a triangular crosssection, any other polygonal
crosssection, or a crosssection that rotates along an axis of the pipe.
In another example, at least one emitter is configured to emit
omnidirectional waves, where at least one ultrasonic transducer element
comprises the at least one ultrasonic emitter and the at least one
ultrasonic receiver, and where the at least one ultrasonic transducer
element is in a configuration determined by a direction of oscillation
relative to waves propagating in the pipe or to an axis of the pipe.
[0017] In another example, the oscillation is along a thickness of the
pipe, where the at least one ultrasonic transducer element is a thickness
mode piezoelectric transducer or a particularlyshaped 13
piezocomposite transducer. In another example, the oscillation is along
the axis of the pipe, where the at least one ultrasonic transducer
element is a circularshaped macrofiber composite with piezoelectric
fibers oriented perpendicular to the axis and comprises electrodes
arranged along the axis of the pipe. In another example, the oscillation
is tangential and orthogonal to the axis of the pipe, where the at least
one ultrasonic transducer element is a circularshaped macrofiber
composite with piezoelectric fibers oriented perpendicular to the axis
and comprises electrodes arranged perpendicular to the axis of the pipe.
In another example, the oscillation is tangential and orthogonal to the
waves, where the at least one ultrasonic transducer element is a
circularshaped macrofiber composite with piezoelectric fibers forming
an annular array and comprises electrodes oriented radially from the
center of the annular array. In another example, the oscillation is
tangential and parallel to the waves, where the at least one ultrasonic
transducer element comprises electrodes forming an annular array, and
where the at least one ultrasonic transducer element is a circularshaped
macrofiber composite with piezoelectric fibers oriented radially from
the center of the annular array.
[0018] In another example, the at least one ultrasonic emitter is
configured to emit waves both unidirectionally and bidirectionally. In
another example, the structure comprises a platelike structure. In
another example, the computing system is further configured to determine
at least one characteristic of one or more flaws in the structure based
at least in part on the following formula:
.PHI. = .phi. .XI. .alpha. [ .PSI. r .PSI.
.theta. .PSI. z ] = [ .psi. T 1 .psi. T2
0  .psi. T 2 .psi. T 1 0 0 0
.psi. z ] [ .differential. .XI. .beta. / .differential.
r 1 r .differential. .XI. .beta. .differential. .theta.
.XI. .beta. ] ##EQU00001##
where .PHI. is a Helmholtz scalar potential, where .PSI..sub.r,
.PSI..sub..theta. and .PSI..sub.z are components of a Helmholtz vector
potential, where .phi., .psi..sub.Tj; j=1,2 and .psi..sub.z are arbitrary
constants, and where .XI..sub..eta.,.eta.=.alpha.,.beta. is a function of
the form exp i(.eta.r cos (.theta..theta..sub.n)+k.sub.zz.omega.t). In
another example, the computing system is further configured to determine
at least one characteristic of one or more flaws in the structure based
at least in part a time delay supplemented by amplitude control based on
a minimum time delay increment, and the minimum time delay is a
characteristic of hardware in the device.
DESCRIPTION OF THE DRAWINGS
[0019] The foregoing aspects and many of the attendant advantages of this
invention will become more readily appreciated as the same become better
understood by reference to the following detailed description, when taken
in conjunction with the accompanying drawings, wherein:
[0020] FIG. 1 depicts an embodiment of acoustic phenomenon corresponding
to uniform axial guided waves;
[0021] FIG. 2 depicts an embodiment of acoustic phenomenon during
traditional focused beam forming;
[0022] FIG. 3 depicts an embodiment of a schematic of a system used for
beam forming and steering;
[0023] FIG. 4 depicts an embodiment a structure with two flaws and how a
second flaw occurring in the shadow of a first, bigger flaw may not be
detected by traditional focused beam forming;
[0024] FIG. 5 depicts an embodiment of unfocused beam forming and steering
of helical guided waves;
[0025] FIG. 6 depicts an embodiment of focused beam forming of helical
guided waves with an eccentric focal point;
[0026] FIG. 7 depicts an embodiment of a method for achieving unfocused
beam forming and steering;
[0027] FIG. 8 depicts an embodiment of a method for achieving for focused
beam forming at an eccentric focal point;
[0028] FIG. 9 depicts an embodiment of an application of focused or
unfocused beam forming of helical guided waves;
[0029] FIG. 10 depicts an embodiment of helical guided waves used to
detect and size second flaw occurring in the shadow of a first, bigger
flaw;
[0030] FIG. 11 depicts an embodiment of helical guided waves and edges of
pipe used to detect and size second flaw occurring in the shadow of a
first, bigger flaw;
[0031] FIG. 12 depicts another embodiment of helical guided waves used to
detect and size second flaw occurring in the shadow of a first, bigger
flaw;
[0032] FIG. 13 depicts an embodiment of helical guided waves and edges of
pipe used to detect an axiallyoriented;
[0033] FIG. 14 depicts an embodiment of a transducer arrangement usable to
detect a flaw using helical guided waves;
[0034] FIGS. 15A and 15B depict, respectively, a side view and an end view
of an embodiment of a transducer element that excites omnidirectional
guided waves by applying forces along the pipe radius;
[0035] FIG. 16 depicts an embodiment of transducer element actuation where
the resulting particle oscillation is axial irrespective of the wave's
helix angle;
[0036] FIG. 17 depicts an embodiment of a macro fiber composite
piezoelectric transducer design configured to achieve the guided waves
depicted in FIG. 16;
[0037] FIGS. 18A and 18B depict a side view and an end view, respectively,
of a transducer element with an actuation that results in wave
propagation with torsional or circumferential particle oscillation;
[0038] FIG. 19 depicts an embodiment of wave propagation where the
particle oscillation is tangential to the pipe but perpendicular to the
helix angle of the guided waves generated by the transducer;
[0039] FIG. 20 depicts an embodiment of a macro fiber composite
piezoelectric transducer design configured to achieve the guided waves
depicted in FIG. 19;
[0040] FIG. 21 depicts an embodiment of wave propagation where the
particle oscillations are parallel to the direction of the helical guided
waves;
[0041] FIG. 22 depicts an embodiment of a macro fiber composite
piezoelectric transducer design configured to achieve the guided waves
depicted in FIG. 21;
[0042] FIG. 23 depicts an embodiment of another transducer array
configured to produce helical guided waves;
[0043] FIG. 24 depicts an embodiment of a method for mapping of flaw from
inspection data;
[0044] FIG. 25 depicts an example chart with dispersion curves for
.gamma.=0.theta..sub.p=0 which are similar to dispersion curves guided
waves in a flat plate;
[0045] FIGS. 26A to 26D depict dispersion curves for guided waves along
helical angles corresponding to, respectively, 0.degree., 30.degree.,
60.degree., and 90.degree., with modes common to all helical angles
marked using circular markers;
[0046] FIGS. 27A to 27D depict wave structure patterns relative to helical
angle at the outer surface of the pipe for the common modes T0, T1, T2,
and T3 T.sub.0, T.sub.1, T.sub.2(as labeled in FIG. 26A) corresponding to
frequencies of, respectively, 0.3 MHz, 0.36 MHz, 0.48 MHz, and 0.67 MHz;
and
[0047] FIGS. 28A and 28B depicts a finite element simulation snapshot of
beam propagating at, respectively, 45.degree. helical angle to the pipe
axis and 60.degree. helical angle to the pipe axis.
DETAILED DESCRIPTION
[0048] This subject matter disclosed herein relates to systems and methods
for unfocussed and focused beam forming and steering of ultrasonic
helical guided waves in pipe and platelike structures. In one
embodiment, a pipelike structure is approximated as a perfectly circular
cylinder that is constructed out of metal, plastic, or inhomogeneous
materials of some regularity, as exemplified by carbon fiber reinforced
polymer (CFRP) composite. Beam forming and steering of ultrasonic helical
guided waves is possible due to formulating guided waves in pipes that
provides improved understanding of the phenomena. In one embodiment, a
system and method directs guided waves along a specific helical angle
providing significant advantages over previous systems and methods.
[0049] The concept of unfocussed beam forming and steering is illustrated
in FIG. 5, where a pipe 58 includes a transducer array 60 configured to
emit rays 62 aligned along a helix over the wall of the pipe 58. A beam
64 of guided waves is generated by controlling the actuation of the
transducer array 60 on the pipe 58 such that the rays 62 are aligned
along a helix over the wall of the pipe 58. In one embodiment, control of
the actuation of the transducer array 60 is achieved by a method
described later with respect to FIG. 7 using a system, such as the
example system depicted in FIG. 3.
[0050] The concept of focused beam forming is illustrated in FIG. 6, where
a beam of guided waves 64 is generated in the pipe 58 so that the beam
comprising helical rays 62 that converge at a focal point 66. In one
embodiment, the focal point 66 is located off the axes of the transducer
array 60 by controlling the actuation of the transducer array 60. The
actuation control in this case is achieved by method described later with
respect to FIG. 8 using a system, such as the example system depicted in
FIG. 3.
[0051] An example method 68 of controlling actuation of the transducer
array for unfocussed beam forming and steering is depicted in FIG. 7.
After the method 68 starts, at block 70, a lookup table of dispersion
surfaces is loaded. The lookup table includes frequency, velocity, and
helix angle combinations obtained by modeling and/or calibration. At
block 72, matching frequency velocity combinations are filtered.
Optionally, at block 74, the helicity can be set at an initial helix
angle, such as 90.degree.. At block 76, a group velocity and a group
helicity are calculated. At block 78, a frequency and velocity of mode
with the lowest group helicity are chosen. At block 80, time delays
and/or amplitudes for each channel are calculated using the chosen
frequency, velocity, helix angle tuple and/or position of transducer. At
block 82, actuation of the transducer array and signal reception are
initiated and synchronized. At block 84, the received ultrasound data is
stored for analysis and/or mapping. At block 86, the helix angle is
incremented. In one embodiment, the helix angle is incremented based on a
desired scan speed and accuracy. At block 88, a determination is made
whether the incremented helicity has reached a final helix angle, such as
90.degree.. If the incremented helicity has not reached the final helix
angle, the method 68 returns to block 72 and repeats steps 72 to 86 for
the incremented helicity. However, if the incremented helicity has
reached the final helix angle, then the method 68 ends.
[0052] An example method 90 of controlling actuation of the transducer
array for focused beam forming is depicted in FIG. 8. After the method 90
starts, at block 92, a lookup table of dispersion surfaces is loaded. The
lookup table includes frequency, velocity, and helix angle combinations
obtained by modeling and/or calibration. At block 94, selected focal
point coordinates on the pipe surface are received. At block 96, the
helicity corresponding to each transducer is calculated relative to the
focal point. At block 98, the matching frequency velocity combinations
for each helicity calculated above are filtered. At block 100, group
velocity and group helicity are calculated. At block 102, the frequency,
phase, and group velocity of mode common to all transducers are chosen.
At block 104, time delays and/or amplitudes are calculated for each pulse
channel. In one embodiment, the delays and/or amplitudes are calculated
based on the chosen frequency, velocity, helix angle tuple and/or
position of the transducers. At block 106, the actuation of the
transducer array and the actuation of signal reception are initiated and
synchronized. At block 108, the received ultrasound data is stored for
analysis and/or mapping. At block 110, a new focal point or an exit
request is received. At block 112, if a new focal point is received, then
the method 90 returns to block 96 and repeats steps 96 to 110 for the new
focal point. However, if an exit request is received, then the method 90
ends.
[0053] In general, ultrasonic transmitters do not need to have direct
access to load carrying layers if the waves can be generated in the
nonloadcarrying layers using a given transmitter. For example, in the
case of a guided wave phased array transducer, the phased array may be
installed on the coated structure (e.g., coated pipe) without removal of
the coating layer. The advantage includes not requiring the full removal
of the coating layer installation of the transducer array a mandatory
practice in conventional methods of installation. This is, in particular,
desirable when the full circumference of the pipeline is not accessible.
Examples of using phased array transducers are described in U.S. Patent
Application No. 62/103,315, filed Jan. 14, 2015, the contents of which
are hereby incorporated by reference in their entirety.
[0054] In addition, in some embodiments, the subject matter disclosed
herein employs mixed time delay and amplitude control to improve beam
forming of high frequency ultrasonic guided waves and thereby further
improve the resolution of the inspection system. As a departure from
traditional apodization methods, the amplitude variation is used to
compensate for the lack of precision in the time delays offered by
current hardware. In some embodiments, the subject matter disclosed
herein may also be used for focused beam forming in platelike
structures. In some embodiments, the subject matter disclosed herein
enables nondestructive scanning of pipelines for flaws of any shape and
orientation at higher speeds with better resolution and improved
accuracy, some of the reasons for which are described in the next
section.
Example Advantages of Disclosed Embodiments
[0055] One of the advantages of the subject matter disclosed herein is
that flaws of all orientations can be detected, located, and sized
simultaneously without necessarily requiring a second stage because of
the variable helical path of the guided waves. Because of the variability
of helical angles, a given flaw can be interrogated from multiple
directions. In some embodiments, the directionality is controlled on
demand by a user or a control algorithm. An example of this capability is
depicted in FIG. 9, where a pipe 114 has a flaw 116 in the form of an
included crack. A transducer array 118 is mounted on the pipe 114. The
transducer array 118 is configured to transmit a helical guided wave
beam, the path of which is represented by ray 120, so that it impinges on
the flaw 116. In the depicted embodiment, the helical guided wave beam
impinges on the flaw 116 at an angle that results in a strong helical
guided wave beam reflection 122. The transducer array 118 is configured
to receive the helical guided wave beam reflection 122.
[0056] Further, due to the reasons that apply to the guided wave focusing
technique (e.g., namely the constructive interference of ultrasound from
multiple transducers), the intensity of the resulting ultrasound will be
high when compared to the first stage of the traditional approach
depicted in FIG. 1. Further, the scanning can be performed at very high
speeds because instead of point by point inspections, the beamformed
wave sweeps long distances as it propagates on a helical path along the
pipeline. In situations where the guided waves attenuate heavily, the
guided wave beam may be made to focus at an eccentric focal point so that
most of advantages of unfocused beam forming and steering are retained
while providing high intensities of traditional focusing methods.
[0057] FIG. 10 depicts an embodiment of helical guided waves used to
detect and size second flaw occurring in the shadow of a first, bigger
flaw. As illustrated, a pipe 124 includes a first flaw 126 and a second
flaw 128. A transducer array 130 is mounted to the pipe 124. The first
flaw 126 is larger than the second flaw 128 and the second flaw 128 is in
the shadow of the first flaw 126 (i.e., the first flaw 126 is located
between the transducer array 130 and the second flaw 128). The transducer
array 130 is configured to transmit a focused or unfocused helical guided
wave beam, the path of which is represented by ray 132, so that it avoids
the first flaw 126 and impinges on the second flaw 128. In the depicted
embodiment, the helical guided wave beam impinges on the second flaw 128
at an angle that results in a helical guided wave beam reflection 134.
The transducer array 130 is configured to receive the helical guided wave
beam reflection 134.
[0058] The hidden flaw may also be detected by observing signals from that
are as a result of multiple reflections, as depicted in FIG. 11. As
illustrated, a pipe 136 includes a first flaw 138 and a second flaw 140.
A transducer array 142 is mounted to the pipe 136. The first flaw 138 is
larger than the second flaw 140 and the second flaw 140 is in the shadow
of the first flaw 138. The transducer array 142 is configured to transmit
a focused or unfocused helical guided wave beam, the path of which is
represented by ray 144, so that it avoids the first flaw 138 and impinges
on the second flaw 140. In the depicted embodiment, the helical guided
wave beam impinges on the second flaw 140 at an angle that results in a
first beam reflection 146. The first beam reflection 146 impinges on an
end of the pipe 136 at an angle that results in a second beam reflection
148. The transducer array 142 is configured to receive the second beam
reflection 148.
[0059] FIG. 12 depicts another embodiment of helical guided waves used to
detect and size second flaw occurring in the shadow of a first, bigger
flaw. As illustrated, a pipe 150 includes a first flaw 152 and a second
flaw 154. A transducer array 156 and a receiver array 158 are mounted to
the pipe 150. The second flaw 154 is in the shadow of the first flaw 152.
The transducer array 156 is configured to transmit a focused or unfocused
helical guided wave beam, the path of which is represented by ray 160, so
that it avoids the first flaw 152 and impinges on the second flaw 154. In
the depicted embodiment, the helical guided wave beam impinges on the
second flaw 154 at an angle that results in a beam reflection 162. The
receiver array 158 is configured to receive the beam reflection 162.
[0060] FIGS. 13 and 14 depict, respectively, another embodiment of the
pipe 136 from FIG. 11 with an axiallyoriented flaw 164 and another
embodiment of the pipe 150 from FIG. 12 with an axiallyoriented flaw
166. In FIG. 13, the helical guided wave beam, as shown by ray 144,
impinges on the axiallyoriented flaw 164 at an angle that results in a
first beam reflection 146. The first beam reflection 146 impinges on an
end of the pipe 136 at an angle that results in a second beam reflection
148. The transducer array 142 is configured to receive the second beam
reflection 148. In FIG. 14, the helical guided wave beam, as shown by ray
160, impinges on the axiallyoriented flaw 166 at an angle that results
in a beam reflection 162. The receiver array 158 is configured to receive
the beam reflection 162. In other embodiments, the example shown in FIGS.
13 and 14 are used to other axiallyoriented features, such seam and
girth welds in pipes. In some embodiments, the systems shown in FIGS. 13
and 14 also have improved resolution due to mixed time and amplitude
control.
[0061] The guided wave beam generated by this direction will be
unidirectional, unlike traditional approaches that are bidirectional. In
other words, traditional approaches generate beams in both directions
along the axis of the pipe. This may be considered an advantage as the
readability of the acquired data is vastly superior because of absence of
reflections from features in one or more directions. However, the
embodiments disclosed herein can optionally be made to act
bidirectionally. In one embodiment, the unidirectional capability is used
for detailed sizing and location of flaws after bidirectional capability
is used to detected the flaws.
[0062] Wave Types and Transducer Designs
[0063] Preliminary results indicate that generation of special wave types
is possible under certain embodiments. In some embodiments, such waves
are generated by particular transducer designs. Some examples of such
waves and transducer design are depicted in FIGS. 15 to 22. A condition
common to transducer element designs is that transducers generate waves
in all directions (i.e., they are omnidirectional). Omnidirectionality
may be achieved when the transducer elements are circular in shape and
conform to the pipe surface, or when the transducer elements are
extremely small so that the liftoff effect due to the pipe's curvature is
negligible.
[0064] FIGS. 15A and 15B depict, respectively, a side view and an end view
of an embodiment of a transducer element that excites omnidirectional
guided waves by applying forces along the pipe radius. As depicted, a
pipe 168 has a transducer element 170 mounted thereon. The transducer
element 170 is configured to emit helical guided waves 172. The helical
guided waves 172 cause particle oscillation 174 in a direction normal to
the wall thickness of the pipe 168. In this embodiment, the transducer
element 170 is a thickness mode transducer that either conforms to the
pipe's surface or is small enough that liftoff of the transducer element
170 from the pipe's surface does not affect the ability of the transducer
element 170 to generate omnidirectional helical guided waves 172. In one
embodiment, the transducer element 170 is a single crystal transducer.
This kind of wave is, however, susceptible to leakage when the pipe 168
is submerged in water and even in situations where the pipe 168 is
covered with of water only on discrete regions.
[0065] FIG. 16 depicts an embodiment of transducer element actuation where
the resulting particle oscillation is axial irrespective of the wave's
helix angle. As depicted, a pipe 176 has a transducer element 178 mounted
thereon. The transducer element 178 is configured to emit helical guided
waves 180. The helical guided waves 180 cause particle oscillation 182 in
an axial direction of the pipe 168. In one embodiment, the axial
actuation is achieved using a macro fiber composite (MFC) piezoelectric
transducer 184 depicted in FIG. 17. As depicted, the MFC piezoelectric
transducer 184 includes closely packed piezoelectric fibers 186 and
electrical current carrying electrodes 188. The piezoelectric fibers 186
in an MFC elongate when electric current is passed through the electrodes
188. The particle displacement 192 (e.g., particle oscillation 182 in
FIG. 16) of the resulting waves 190 (e.g., helical guided waves 180 in
FIG. 16) continue to be along the direction that the piezoelectric fibers
186 elongate. The circular pattern of the overall transducer 184 ensures
that omnidirectional guided waves 190 (e.g., helical guided waves 180 in
FIG. 16) are generated.
[0066] FIGS. 18A and 18B depict a side view and an end view, respectively,
of a transducer element with an actuation that results in wave
propagation with torsional or circumferential particle oscillation. As
depicted, a pipe 194 has a transducer element 196 mounted thereon. The
transducer element 196 is configured to emit helical guided waves 198.
The helical guided waves 198 cause torsional or circumferential particle
oscillation 200. In one example, the embodiment shown in FIGS. 18A and
18B can be achieved using the MFC piezoelectric transducer 184 depicted
in FIG. 17 at an angle rotated by about 90.degree. from the orientation
of the transducer element 178 depicted in FIG. 16.
[0067] FIG. 19 depicts an embodiment of wave propagation where the
particle oscillation is tangential to the pipe but perpendicular to the
helix angle of the guided waves generated by the transducer. As depicted,
a pipe 202 has a transducer element 204 mounted thereon. The transducer
element 204 is configured to emit helical guided waves 206. The helical
guided waves 206 cause particle oscillation 208 tangential to the pipe
202 but perpendicular to the helical guided waves 206. In one embodiment,
the particle oscillation 208 is achieved using a macro fiber composite
(MFC) piezoelectric transducer 210 depicted in FIG. 20. As depicted, the
MFC piezoelectric transducer 210 includes closely packed piezoelectric
fibers 212 and electrical current carrying electrodes 214. The
piezoelectric fibers 212 in an MFC elongate when electric current is
passed through the electrodes 214. The particle displacement 218 (e.g.,
particle oscillation 208 in FIG. 19) of the resulting waves 216 (e.g.,
helical guided waves 206 in FIG. 19) continue to be along the direction
that the piezoelectric fibers 186 elongate (i.e., normal to the resulting
waves 216). The circular pattern of the overall transducer 210 ensures
that omnidirectional guided waves 216 (e.g., helical guided waves 206 in
FIG. 19) are generated. In other embodiments, the MFC piezoelectric
transducer 210 can have a patter that is a portion of a circle, such as a
semicircular design.
[0068] FIG. 21 depicts an embodiment of wave propagation where the
particle oscillations are parallel to the direction of the helical guided
waves. As depicted, a pipe 220 has a transducer element 222 mounted
thereon. The transducer element 222 is configured to emit helical guided
waves 224. The helical guided waves 224 cause particle oscillation 226
tangential to the pipe 220 and parallel to the helical guided waves 224.
In one embodiment, the particle oscillation 226 is achieved using a macro
fiber composite (MFC) piezoelectric transducer 228 depicted in FIG. 21.
As depicted, the MFC piezoelectric transducer 218 includes closely packed
piezoelectric fibers 230 and electrical current carrying electrodes 232.
The piezoelectric fibers 230 in an MFC elongate when electric current is
passed through the electrodes 232. The particle displacement 236 (e.g.,
particle oscillation 226 in FIG. 21) of the resulting waves 234 (e.g.,
helical guided waves 224 in FIG. 21) continue to be along the direction
that the piezoelectric fibers 186 elongate (i.e., normal to the resulting
waves 216). The circular pattern of the overall transducer 228 ensures
that omnidirectional guided waves 236 (e.g., helical guided waves 226 in
FIG. 21) are generated. In other embodiments, the MFC piezoelectric
transducer 228 can have a patter that is a portion of a circle, such as a
semicircular design.
[0069] Transducer arrays do not need to be of the shape illustrated in
FIG. 5 or 6. FIG. 23 depicts an embodiment of another transducer array
configured to produce helical guided waves. As depicted, a pipe 238
includes a transducer array 240 configured to emit rays 244 aligned along
a helix over the wall of the pipe 238. A beam 242 of guided waves is
generated by controlling the actuation of the transducer array 240 on the
pipe 238 such that the rays 244 are aligned along a helix over the wall
of the pipe 238. Transducer arrays usable with the embodiments disclosed
herein are not limited to the transducer arrays depicted in FIGS. 5, 6,
and 23, but can take any number of other shapes.
[0070] Array Control Parameters
[0071] The first step of the algorithms illustrated in FIG. 7 and FIG. 8
includes loading a lookup table that may be generated by a modeling
method (such as those detailed below), by a calibration method, or by a
combination thereof. Both methods of generating the lookup tables have
their advantages and disadvantages. Modeling methods have the advantage
of giving an estimate of the how the particle oscillation of a wave might
be. This enables modification of transducer design, as discussed below.
However, the calculations involved in modeling methods are based on the
assumptions of fixed material properties. It is well known that,
irrespective of manufacturing process, structures have a statistical
variation in properties. Calibration methods overcome this drawback.
However, the data from calibration methods are specific to the particular
hardware used. In in certain embodiments, the lookup table will be a
combination of modeling methods and will be corrected with the help of
calibration.
[0072] In FIG. 7 and FIG. 8, the term helicity stands for the angle formed
by the helical path relative to the pipe axis when the pipe's cylindrical
surface is unwrapped into a planar surface. Typically, the ray forms a
straight line on this unwrapped surface in which case the helicity is
constant. The term linear helicity may be used to describe this kind of
helicity. However, it is possible that the waves may have a varying or
nonlinear helicity. In other words, the ray may form a curve on the
planar surface. Such waves can be used for augmenting the hidden flaw
detection capability of this invention.
[0073] The term group velocity in FIG. 7 and FIG. 8 is the apparent
velocity of a beam. The term group helicity in FIG. 7 and FIG. 8 can be
explained as the manifestation tendency of a beam to change its direction
towards one that nature mandates as the easiest path. This is possible in
pipes made of any material. However, such a phenomenon will be observed
more frequently in case of structures made from the socalled anisotropic
materials, such as carbon fiber reinforced polymer composite. If the
group helicity is different from the desired beam helicity, it can be
both advantageous and disadvantageous from the point of view inspection.
A different group helicity will add to the nonlinearity of the helical
guided wave, helping detection and sizing of hidden flaws. On the flip
side however, such beams tend to disperse away as they continue
propagating, rendering it useless for long distance inspection.
[0074] As a departure from traditional methods, mixed time delay and
amplitude control may be used to achieve high frequency guided wave
propagation. Such a mixing of time delays and amplitude variation has
been suggested in literature without taking into account the fact that
the minimum time delay offered by hardware limits the frequency at which
good quality beam forming is achieved. Time delays can be completely
replaced by amplitude variation across the transducer elements. Further,
amplitude control can be expressed in terms of time delay. Changing of
time delays is much faster than amplitude change, particularly if the
change in amplitude is large in value. In some of the embodiments
disclosed herein, time delays may be used as much as possible. However,
when the minimum time delay increment is not sufficiently small,
amplitude control may be used to correct the deficiency. In such a
scenario the amplitude change may be small and can be achieved at very
high speeds. This will improve the resolution of the inspection system in
proportion to the frequency that becomes possible.
[0075] Flaw Characterization
[0076] Flaw characterization involves the determination of one or more of
the existence, location, size, shape and orientation of any flaw.
Features that can be characterized as flaws include inclusions, cracks,
corrosion, dents, attachments, welds, or any other type of nonuniform
feature. The characteristics of the flaws will be extracted from the
ultrasonic data received by the elements of transmitter array, a
traveling or scanning receiver sensor, and/or a dedicated receiver array
consisting of at least one sensor element that may be placed anywhere on
the pipe. The receiver array, if any, may have its sensor elements
distributed in any fashion, for example they may be distributed
circumferentially or linearly. The signatures that help determine the
existence of a flaw correspond to reflection of ultrasound from a flaw
and/or an unexpected absence of ultrasonic signals. In one embodiment,
the location is determined by taking into account the helical angle at
which ultrasonic beam is launched at the transmitter and, in case of a
signature caused due to reflection of ultrasound from a flaw, the
properties of signature (e.g., its amplitude distribution in time or
frequency domain), its arrival time relative to the time at which the
beam was launched, or the helix angle of the reflected beam when it was
received.
[0077] The helix angle of the received reflection signal can be determined
by several methods. In case of single receiver, the original transmit
helix angle, the relative location of the receiver and arrival time of
the received signal may be used to triangulate the location of the flaw.
If a receiver is used, then, in addition signal processing methods (e.g.,
Fourier transforms) may be used to determine the angle of arrival. In all
of the calculations, the lookup table is calculated using the theory
discussed below. An example method 246 for mapping and/or obtaining a
scanned image of pipe is illustrated in FIG. 24.
[0078] The method 246 beings with three steps that can be performed in
series or in parallel. At block 248, a dataset variable is set to an
initial value, such as D=1. At block 450, stored datasets are retrieved.
In some embodiments, the stored datasets are retrieved using the methods
depicted in FIGS. 7 and 8. At block 252, a grid representing a defect map
of the pipe is initiated. At block 254, a dataset corresponding to the
dataset variable is extracted. At block 256, a determination is made
whether the dataset variable has been incremented to the end of the
database. If the dataset variable has been incremented to the end of the
database, then the method 246 ends. If the dataset variable has not been
incremented to the end of the database, then the method 246 continues to
block 258.
[0079] At block 258, a helix angle of arrival and intensity of patterns
are calculated. In one embodiment, the helix angle of arrival and the
intensity of patterns are calculated using Fourier transforms and/or
receiver array data. At block 260, a determination is made whether an
anomalous pattern exists. If no anomalous pattern exists, then the method
246 proceeds to block 262 where the dataset variable is incremented and
then the method 246 returns to block 254. However, if an anomalous
pattern exists, the method 246 proceeds to block 264. At block 264, a
helix angle of arrival and an intensity of patterns are calculated. In
one embodiment, the helix angle of arrival and the intensity of patterns
are calculated using Fourier transforms and/or receiver array data. At
block 266, the defect is triangulated and characterized and corresponding
values are transferred to a defect map. In some embodiments, the defect
is triangulated and characterized using a mean helix angle of generation,
the distance between transmitter array and receiver element at which
anomaly was detected, and/or the angle of arrival of anomaly and look up
table of velocities. The method 246 then proceeds to block 262 where the
dataset variable is incremented and then the method 246 returns to block
254.
[0080] Other Applications
[0081] The embodiments disclosed herein may be used for applications
employing ultrasonic guided waves that achieve improved performance in
the presence of high intensity ultrasound. Examples of such applications
include nonlinear ultrasonic testing, ultrasonic deicing, ultrasonic
cleaning, and processing involving sonochemistry.
[0082] As already mentioned, the subject matter disclosed herein includes
methods for unfocussed and focused beam forming and steering of helical
guided waves. The methods depicted in FIGS. 7 and 8 can be used for
synthetic unfocused beam forming and synthetic focused beam forming,
respectively; collectively called herein as synthetic beam forming.
Synthetic beam forming includes application of methods similar to those
depicted in FIGS. 7 and 8 to the set of signals (a) received individually
by each receiver element of the receiver array, (b) received by a single
receiver element but which originate from waves sequentially transmitted
by each element of a transmitter array such that the corresponding waves
do not interfere with one another for a desired or specified duration, or
(c) a combination of both independent reception by the receiver elements
and sequential generation (or transmission) by the transmitter array
elements. In some embodiments, synthetic beam forming mimics the effects
of real beam forming. If there are N receiver element and M transmitter
elements, the total number of data sets for each type of synthetic beam
forming approach will be N, M and N.times.M. This combined approach may
be called a synthetic aperture imaging of the pipe using helical guided
waves. In one embodiment, both of those methods depend on a lookup table
of parameters such as frequency, velocity and helix angle combinations at
which helical guided wave propagation is possible. In some embodiments,
these parameters are evaluated using the theory discussed below. However,
while the theory below is presented for isotropic media, the concepts can
be extended to anisotropic materials such as crystals, rolled metals, and
carbon fiber reinforced composites.
[0083] Bulk Wave Solutions
[0084] The governing equation for elastic wave propagation in an isotropic
elastic medium is given by the balance of momentum and the Hooke's Law,
which are respectively expressed as follows:
.gradient. .sigma. = .rho. .differential. 2 u
.differential. t 2 1 a .sigma. = .lamda.
tr ( .epsilon. ) I + .mu. .epsilon. 1 b
##EQU00002##
[0085] where, .sigma. is the stress tensor, u is the particle displacement
vector and .epsilon.=(.gradient.u+.gradient.u.sup.T)/2 is the strain
tensor and t is time. Combine Equations 1a and 1b the final equation of
motion (or Navier's equation) is obtained as follows:
( .lamda. + .mu. ) .gradient. ( .gradient. u ) +
.mu. .gradient. .gradient. u = .rho. .differential. 2
u .differential. t 2 2 ##EQU00003##
[0086] In order to solve Equation 2 the Helmholtz decomposition of u is
employed that can be expressed as follows:
u=.gradient..PHI.+.gradient..times..PSI. 3a
.gradient..PSI.=f(r,t) 3b
where, .PHI. and .PSI. are the Helmholtz scalar and vector potentials;
f(r, t) is an arbitrary function and in terms of physical components with
respect to the cylindrical coordinate system (r, .theta., z), Equations
3a and 3b are
u r = .differential. .PHI. .differential. r + 1 r
.differential. .PSI. z .differential. .theta.  .differential.
.PSI. .theta. .differential. z 3 c u .theta. =
1 r .differential. .PHI. .differential. .theta. +
.differential. .PSI. r .differential. z  .differential. .PSI. z
.differential. r 3 d u z = .differential.
.PHI. .differential. z + 1 r .differential. r .PSI.
.theta. .differential. r  1 r .differential. .PSI. r
.differential. .theta. 3 e 1 r
.differential. r .PSI. .theta. .differential. r + 1 r
.differential. .PSI. r .differential. .theta. +
.differential. .PSI. z .differential. z = f ( r , t )
3 f ##EQU00004##
[0087] The Equation 3b is also called as Helmholtz' gauge invariance
criterion. Substituting Equation 3a in Equation 2, the latter can be
decomposed into a system of 4 partial differential equations, given by
.gradient. 2 .PHI.  1 c 1 2 .differential. 2
.PHI. .differential. t 2 = 0 4 a .gradient. 2
.PSI. r  1 r 2 .PSI. r  2 r 2 .differential.
.PSI. .theta. .differential. .theta.  1 c 2 2
.differential. 2 .PSI. z .differential. t 2 = 0 4
b .gradient. 2 .PSI. .theta.  1 r 2 .PSI. .theta.
 2 r 2 .differential. .PSI. r .differential. .theta. 
1 c 2 2 .differential. 2 .PSI. z .differential. t 2
= 0 4 c .gradient. 2 .PSI. z  1 c 2 2
.differential. 2 .PSI. z .differential. t 2 = 0 4
d ##EQU00005##
[0088] where, the scalar Laplacian operator .gradient..sup.2 is given by
.gradient. 2 = .differential. 2 .differential. r 2 +
1 r .differential. .differential. r + 1 r 2
.differential. 2 .differential. .theta. 2 + .differential. 2
.differential. z 2 5 ##EQU00006##
[0089] Assuming a trial solution, .PHI.=.phi.e.sup.i(.alpha.r cas
.theta.+k.sup.z.sup.z.omega.t) where .phi. is an arbitrary constant and
substituting in Equation 4a it can be shown
(  .alpha. 2 + k z 2  .omega. 2 c 1 2 ) .phi. =
0 6 a ##EQU00007##
[0090] For a non trivial .phi.,
.alpha. 2 = k z 2  .omega. 2 c 1 2 6 b
##EQU00008##
[0091] Similarly, assuming the trial solution .PSI..sub.z=.psi..sub.z
e.sup.i(.beta.r cos .theta.+kz.omega.t), .psi..sub.z being an arbitrary
constant, and substituting in Equation 4d the following can be
demonstrated.
(  .beta. 2 + k z 2  .omega. 2 c 2 2 ) .psi. z
= 0 6 c .beta. 2 = k z 2  .omega. 2 c 2 2
6 d ##EQU00009##
[0092] Let .XI..sub..beta. be any function that also satisfies Equation
4d. Differentiating Equation 4d with respect to r and substituting
.PSI..sub.z=.XI..sub..beta., the following equation is obtained:
.differential. 3 .XI. .beta. .differential. r 3  1
r 2 .differential. .XI. .beta. .differential. r + 1 r
.differential. 2 .XI. .beta. .differential. r 2  2 r 3
.differential. 2 .XI. .beta. .differential. .theta. 2 +
1 r 2 .differential. 3 .XI. .beta. .differential. r
.differential. .theta. 2 + 1 r 2 .differential. 3
.XI. .beta. .differential. r .differential. z 2  1 c 2
2 .differential. 3 .XI. .beta. .differential. r
.differential. t 2 = 0 7 ##EQU00010##
[0093] Using Equation 7, it can be shown that Equations 4b and 4c are
simultaneously satisfied if the .PSI..sub.r and .PSI..sub..theta. have
the following form:
[ .PSI. r .PSI. .theta. ] = [ .psi. T 1
.psi. T2  .psi. T 2 .psi. T 1 ]
[ .differential. .XI. .beta. .differential. r 1 r
.differential. .XI. .beta. .differential. .theta. ] 8
##EQU00011##
where, as before .psi..sub.Tj; j=1,2 are arbitrary constants and the
subscript T stands for the term transverse. It may be noted that the
expressions e.sup.i(.alpha.r cos .theta.+kz.omega.t) and e.sup.i(.beta.r
cos .theta.+kz.omega.t) represent plane waves propagating in the xz
plane. The solutions presented thus far can be modified to the more
general case of a plane wave propagating at any orientation in the
r.theta. plane. Before proceeding in this direction, new notations need
to be introduced, viz. .XI..sub..theta.=e.sup.i(.eta.r
cos(.theta..theta..eta.)+k.sup.z.sup.z.omega.t), where .eta.=.alpha.,
.beta..sub.Z, .beta..sub.T. Using this new scheme of notation, the
solutions are recapitulated as follows:
.PHI. = .phi. .XI. .alpha. 9 a [
.PSI. r .PSI. .theta. .PSI. z ] = [ .psi. T
1 .psi. T 2 0  .psi. T 2 .psi. T
1 0 0 0 .psi. z ] [ .differential. .XI.
.beta. T / .differential. r 1 r .differential. .XI.
.beta. T .differential. .theta. .XI. .beta. z ] 9
b ##EQU00012##
where, although .beta..sub.Z=.beta..sub.T=.beta. that
.theta..sub..beta..sub.z.noteq..theta..sub..beta..sub.T which further
generalizes the solutions. It may be verified that this does not affect
the consistency of equations thus far.
[0094] The final step before writing down the most general solution for
.PHI. and .PSI., it is necessary to consider the Helmholtz gauge
invariance criterion (Equation 3b). The choice of f (r, t) on the right
hand side of Equation 3b is arbitrary. It can be shown that f (r, t)
vanishes whenever .theta..sub..beta..sub.Z=.theta..sub..beta..sub.T, in
which case Equation 3b reduces to:
(.beta..sup.2.psi..sub.T1+ik.sub.z.psi..sub.z).XI..sub..beta.=0 10
[0095] From here on the convention
.XI..sub..beta..sub.T=.XI..sub..beta..sub.T=.XI..sub..beta. will be
employed. The general solution for .PHI. and .PSI. can be written as:
.PHI. = [ .phi. + .XI. + .alpha. + .phi. 
.XI.  .alpha. ] ( kz  .omega. t )
11 a [ .PSI. r .PSI. .theta. .PSI. z ] =
[ k z .beta. 2 .psi. z + .psi. T 2
+ 0  .psi. T 2 + k z .beta. 2
.psi. z + 0 0 0 .psi. T 2 + ] [
.differential. .XI. + .beta. .differential. r 1 r
.differential. .XI. + .beta. .differential. .theta. .XI. +
.beta. ] + [ k z .beta. 2 .psi. z 
.psi. T 2  0  .psi. T 2 
k z .beta. 2 .psi. z  0 0 0 .psi. T 2 
] [ .differential. .XI.  .beta. .differential. r
1 r .differential. .XI.  .beta. .differential. .theta.
.XI.  .beta. ] 11 b ##EQU00013##
where, .XI..sub..eta.=e.sup.i.eta.r
cos(.theta.),.eta.=.+..alpha.,.+..beta.; .phi..sup..+. and
.psi..sub.m.sup..+.,m=T2,z are arbitrary coefficients corresponding to
.+..alpha. and .+..beta., respectively. For convenience the number "2"
in the subscript T2 will be dropped from the equations henceforth.
Substituting Equations 12a and 12b in Equations 3a3c, the expressions
for the particle displacement vectors can be obtained as follows:
[ u r u .theta. u z ] = U + X + + U
 X  [ .phi. + .XI. + .alpha. .psi. T +
.XI. + .beta. .psi. z + .XI. + .beta. ]
where , 12 a U .+. = [ .+. .alpha. C
.alpha. .+. k z .beta. C .beta. .+. ( 1
+ k 2 .beta. 2 ) .beta. S .beta. .+.
.alpha. S .alpha. .+. k z .beta. S .beta.
.+. ( 1 + k 2 .beta. 2 ) .beta. C .beta.
k z .beta. 2 0 ] 12 b X .+. =
[ .phi. + .XI. + .alpha. .psi. T + .XI. + .beta.
.psi. z + .XI. + .beta. ] where , C
.eta. = cos ( .theta.  .theta. .eta. ) and S
.eta. = sin ( .theta.  .theta. .eta. ) = .eta. = .alpha.
, .beta. . 12 c ##EQU00014##
[0096] Formulation for Guided Waves
[0097] The field of guided wave propagation in isotropic pipes includes as
study of several fundamental problems including propagation in rods,
submerged pipes, fluid carrying pipes and multilayered pipes. For the
sake of simplicity, only the formulation and analysis of guided waves in
a single layered pipe is presented.
[0098] For modeling guided waves the traction vector components on the
pipe surface are required and are given by:
[ .sigma. rr .sigma. r .theta. .sigma. rz
] = D + X + + D  X  where , 13 a
D .+. = [  ( .lamda..omega. 2 / c 1 2 + 2
.mu..alpha. 2 C .alpha. 2 )  2 .mu. k z
.beta. 2 C .beta. 2 2 .mu. ( 1 + k z 2 .beta. 2
) .beta. 2 S .beta. C .beta. 2 .mu..alpha. 2
S .alpha. C .alpha. 2 .mu..beta. 2 S .beta.
C .beta. .mu. ( 1 + k z 2 .beta. 2 ) .beta. 2
( C .beta. 2  S .beta. 2 ) .+. 2 .mu. k z
.alpha. C .alpha. .+. .mu. ( .beta. 2 
k z 2 ) .beta. C .beta. .+. .mu. ( 1 + k z 2
.beta. 2 ) k z .beta. S .beta. ] 13 b
##EQU00015##
[0099] General Solution: Nonlinear Helicity
[0100] For a singlelayered pipe the formulation is achieved by traction
free boundary conditions at both the surfaces of the pipe. Let the pipe
wall thickness be 2.DELTA.R and the mean radius of the pipe wall be given
by R. Substitution of vanishing traction vectors in Equation 13,
evaluated at R+.DELTA.R and R.DELTA.R, the following expression is
obtained
GX = [ D ( + ) E ( + ) D (  ) E (  )
D ( + ) E (  ) D (  ) E ( + ) ] [
X + ( R ) X  ( R ) ] = [ 0 0 ]
14 ##EQU00016##
where E.sup..+. stands for the diagonal matrix whose entries are given
by e.sup..+.i.alpha..DELTA.R cos .theta., e.sup..+.i.beta..DELTA.R cos
.theta. and e.sup..+.i.beta..DELTA.R cos .theta., respectively. For
nontrivial X, the following condition must be satisfied:
.GAMMA.:=det[G]=0 15
where det[G] stands for the determinant of the matrix G.
[0101] Equation 15 is termed as the dispersion relation that may be solved
for different combinations of
.theta.,.theta..sub..alpha.,.theta..sub..beta.. For each such combination
dispersion curves that are a function of .omega., k are obtained. For
each point on the dispersion curve, Equation 15 may be numerically solved
for X.sup.(.+.)(R), from which the arbitrary coefficients
.phi..sup..+., .psi..sub.T.sup..+., .psi..sub.z.sup..+. and
subsequently, the displacement and traction components may be evaluated.
It will be shown later that for some special cases analytical expressions
for the dispersion curves are possible. For further discussion the
following new notation is introduced:
g.sub.z=g.sub.z(.theta.,.omega.): ={k.sub.z:
.GAMMA.(k.sub.z,.theta.,.omega.)=0} 16
where, g.sub.z is the wavenumber of guided wave (which is denoted by the
superscript). Equation 17 makes explicit an otherwise implicit assumption
in guided wave modeling that in general the axial wavenumber, k.sub.z is
an independent quantity while g.sub.z, the wavenumber of the guided waves
are given by a subset of values of k.sub.z that satisfy Equation 15 and
that therefore, g.sub.z does not remain an independent quantity. This
notion or notation is used in subsequent derivations to avoid confusion,
particularly when differentiation with respect to wavenumbers is
involved.
[0102] The phase of the guided wave may therefore be expressed as
P=g.sub.zz.omega.t. The phase, P represents the guided wave front
whenever it is constant. Thus its derivative relative to time results the
following expression:
P t = .differential. P .differential. z z
t + 1 r .differential. P .differential. .theta. r
.theta. t  .omega. = 0 17 a ##EQU00017##
[0103] The coefficients of the time derivatives in Equation 17 give the
wavevector components, one of which is
g z = .differential. P .differential. z ##EQU00018##
that can be evaluated by solving Equation 16. The other coefficient gives
the wavevector along the circumferential direction and may be expanded
as follows:
g .theta. = 1 r .differential. P .differential. .theta.
= z r .differential. g z .differential. .theta. 17
b ##EQU00019##
where g.sub..theta. is the angular wavenumber. The phase helical angle,
.theta..sub.p that is defined here as the anglemeasured relative to
zaxis on circular sheet or radius r on a pipealong which a wave of
monochromatic frequency is travelling is given by the relation
tan .theta. _ p = g .theta. g z 17 c
##EQU00020##
[0104] Equations 18b and 18c show that the angular wavenumber of the
guided wave is dependent on the axial distance as well. Since g.sub.z is
independent of z, it follows that the helical guided waves may tend to
become circumferential guided waves. Thus the solutions in this section
indicate the possibility of guided waves with nonlinear helicity. It
will be numerically shown later that most guided waves of nonlinear
helicity are lossy and will therefore propagate only over short axial
distances.
[0105] Although the components of phase velocity may be expressed as
c z = .omega. g z , c .theta. = g .theta. , ##EQU00021##
phase velocity is a term that is frequently used in guided wave
literature, in most practical scenarios, the group velocity is the more
important and directly measurable quantity. The corresponding components
of group velocity .nu..sub.z, .nu..sub..theta. are given by:
v z = .differential. .omega. .differential. g z 18 a
v .theta. = .differential. .omega. .differential. g .theta.
18 b ##EQU00022##
[0106] Consequently, we may define a group helical angle, .theta..sub..nu.
as follows:
tan .theta. _ v := v .theta. v z 19
##EQU00023##
[0107] The group helical angle has thus far not been reported in
literature. The concept is analogous to skewing of guided waves
propagating in an anisotropic plate.
[0108] With these general derivations, it may be inferred that wave
propagation in pipes may be more complex than it is otherwise thought to
be. The formulation presented till now allows several inferences that are
not as straightforward when using Bessel's function based solutions to be
made. The first nontrivial inference that can be drawn from Equations 14
and 15 is that the dispersion relation propagation in a pipe does not
depend upon the mean radius of the pipe. The effect of curvature is
however, manifested through the dependence of G on .theta.. The
dispersion curves will scale relative to the wall thickness, a feature
that is also observed in case of plates. In the subsequent section
formulation restricted to guided waves of linear helicity will be
presented.
[0109] Guided Waves of Linear Helicity
[0110] For the analysis of guided waves of linear helicity, consider the
terms representing the phases of .XI..sub..alpha. and .XI..sub..beta.:
P.sub..alpha.=.alpha.r cos(.theta..theta..sub..alpha.)+k.sub.z.omega.t
20a
P.sub..beta.=.beta.r cos(.theta..theta..sub..beta.)+k.sub.z.omega.t
20b
[0111] The corresponding wavevectors are obtained by taking the vector
gradient of the Equations 20a and 20b which in component form are:
k.sub..alpha.=[.alpha. cos(.theta..theta..sub..alpha.), .alpha. sin
.theta..theta..sub..alpha.,k.sub.z].sup.T 21a
k.sub..beta.=[.beta. cos .theta..theta..sub..beta., .beta. sin
.theta..theta..sub..beta.,k.sub.z].sup.T 21b
[0112] The quantities enumerated in the vectors in Equations 21a and 21b
are the radial, circumferential and axial wavenumbers, respectively. To
provide a relationship between .theta..sub..alpha. and .theta..sub..beta.
the following relationship is enforced:
.alpha. sin .theta..theta..sub..alpha.=.beta. sin
.theta..theta..sub..beta.=k.sub..theta. 23
[0113] That is the tangential components of the wavevector are unique,
which is an extension of the concept from two and three dimensional plate
guided wave theory. If this rule is violated then as also observed in the
previous section, the wave propagation will be attenuated because of
destructive interference of the waves.
[0114] Using Equation 19, introducing the notations, .alpha.:=.alpha.
cos(.theta..theta..sub..alpha.)= {square root over
(.alpha..sup.2k.sub..theta..sup.2)} and .beta.:=.beta. cos
.theta..theta..sub..beta.= {square root over
(.beta..sup.2k.sub..theta..sup.2)}; the formulation for guided waves
will remain similar except for the following:
U .+. = [ .+. .alpha. _ .+. k z
.beta. _ .+. ( 1 + k 2 .beta. 2 ) k .theta.
.+. k .theta. .+. k z k .theta. .+.
( 1 + k 2 .beta. 2 ) .beta. _ k z
.beta. 2 0 ] 24 a D .+. = [  (
.lamda..omega. 2 / c 1 2 + 2 .mu. .alpha. _ 2 )  2
.mu. k z .beta. _ 2  2 .mu. ( 1 + k z 2
.beta. 2 ) k .theta. .beta. _  2 .mu. k
.theta. .alpha. _  2 .mu. k .theta.
.beta. _ .mu. ( 1 + k z 2 .beta. 2 ) ( .beta. _
2  k .theta. 2 ) .+. 2 .mu. k z .alpha. _
.+. .mu. ( .beta. 2  k z 2 ) .beta. _ .+.
.mu. ( 1 + k z 2 .beta. 2 ) k z k .theta. ]
24 b .XI. .+. .eta. = .eta. _ r ,
.eta. = .alpha. , .beta. 24 c ##EQU00024##
[0115] Note that for numerical stability, it is advisable to replace
D.sup..+. with D.sup..+.=.beta..sup.2 D.sup..+. in order to remove the
.beta..sup.2 term from the denominator. For the sake of brevity, however,
this will not be explicitly done here. Analogous to Equation 17 the wave
vector of the guided wave is given by:
g.sub..theta.=k.sub..theta. 25a
g.sub.z=g.sub.z(g.sub..theta.,.omega.):={k.sub.z:.GAMMA.(k.sub.z,g.sub..
theta.,.omega.)=0} 25b
Alternately,
g.sub.z=k.sub.z 25c
g.sub..theta.=g.sub..theta.(g.sub.z,.omega.):={k.sub.z:
.GAMMA.(g.sub.z,k.sub..theta.,.omega.)=0} 25d
[0116] Thus linear helical guided waves are independent of the physical
angle .theta.. This suggests that the dispersion relations for guided
wave in pipe may be equivalent to those in plates. The formulation in
this section may also be interpreted to mean that due to the phenomenon
of interference the orientations, .theta..sub..alpha., and
.theta..sub..beta. of the partial waves change as the guided wave of
linear helicity propagates along the corresponding helical path.
[0117] For the purpose of generating the lookup table as illustrated in
the flowcharts (e.g., in FIGS. 7 and 8), it is desirable to evaluate the
wave number g.sub.p along and helix angle .theta..sub.p. This may be
achieved by setting k.sub..theta.=k sin(.theta..sub.p) and k.sub.z=k cos
(.theta..sub.p) and then solving equation 16 for k. This may be
mathematically stated as:
g.sub.p=g.sub.p(.theta..sub.p,.omega.):={k:
.GAMMA.(k,.theta..sub.p,.omega.)=0} 26
[0118] Subsequently, the group velocity components v.sub.v and v.sub.t
along the helix angle .theta..sub.p and the transverse direction
.pi./2.theta..sub.p, may be evaluated in a manner that is analogous to
Equations 19a and 19b and are given by
v p = .differential. .omega. .differential. g p 27 a
v t = 1 g .differential. .omega. .differential. .theta.
_ p 27 b ##EQU00025##
[0119] Consequently, we may define a group helical skew angle,
.theta..sub.s as follows
tan .theta. _ s := v t v p 28 ##EQU00026##
[0120] The skew angle, .theta..sub.s is a direct measure of the angle by
which a helical guided wave beam will deviate from the helix angle,
.theta..sub.p when generated using a pulsed excitation.
[0121] A particular case of helical guided wave propagation is the
circumferential guided wave for which .theta..sub.p=.pi./2 or in other
words, k.sub.z=0. Results from traditional approaches suggest that the
circumferential wavenumber is proportional to the radius of the pipean
aspect that is not observed in the current formulation.
[0122] Numerical Results
[0123] In this section, numerically calculated dispersion properties
corresponding to some helical angles including axial guided waves and
circumferential guided waves will be explored. The example case of a
steel pipe of 8.4 mm wall thickness is considered. The bulk longitudinal
velocity, c.sub.1 and the bulk shear velocity, c.sub.2 and the density,
.rho. are assumed to be 5.94 mm/.mu.s, 3.25 mm/.mu.s and 7.8 g/cc;
respectively. The dispersion curves were traced using Muller's method.
[0124] First, consider the phase velocity dispersion curves corresponding
to axially propagating modes (.theta..sub.p=0), shown in FIG. 25, which
includes all the different types of modes that are traditionally
classified as longitudinal, flexural and torsional modes. As already
mentioned, the dispersion curves for pipes are identical to the
dispersion curves in a flat plate that are analogously classified as
symmetric, antisymmetric and shear horizontal modes. This equivalence of
axiallypropagating pipe guided waves and plate guided waves is in
conformity with the traditional knowledge.
[0125] The variation of the dispersion curves for guided waves along
0.degree., 30.degree., 60.degree. and 90.degree. helical angles are
illustrated in FIGS. 26A to 26D. As highlighted in FIGS. 26A to 26D, the
modes that resemble torsional modes (e.g., in the case of axial guided
waves) are common to all helical angles of propagation. These common
modes are also labeled as T.sub.0, T.sub.1, T.sub.2 and T.sub.3 in FIG.
26A. In the case of 30.degree. and 60.degree. helical angles, the modes
that are not common to all helical angles correspond to complex valued
roots of the dispersion relation. It can be therefore inferred that these
modes will propagate over limited distances depending on the value of the
imaginary part (i.e., they will propagate but will eventually attenuate).
This inference is nonintuitive because a lossless system (Equations 1a
and 1b) is assumed herein and one may expect either real or imaginary
(nonpropagating) modes as is typical in the case of Bessel function
based approach for pipe guided waves as well as in the case of plate
guided wave theory. This prediction of attenuative but propagating modes
can be explained by comparing the current formulation with the
traditional Bessel function based formulation. Traditional
Besselfunctionbased solutions inherently predict helical guided wave
modes that propagate with radially varying helical angles. In other
words, the characteristic of these modes is to diverge as they propagate
along a mean helical angle. This divergence will cause the modes to
eventually dissipate with a severity that is directly and inversely
proportional to the pipe's wall thickness and its midradius,
respectively. The current formalism that is based on constant helical
angle distribution therefore appears to account for this divergence (and
hence dissipation) of such modes by predicting them to be in effect
attenuative. It may be noted that this is merely a conjecture and further
analysis is necessary to relate the respective modal characteristics of
the current and traditional formulations.
[0126] For designing transducers for generation and reception of helical
guided waves, it is important to investigate the respective distribution
of particle displacement vector components (or "wavestructure") of the
guided wave modes with the variation in helical angle. The comparison is
restricted to only the modes that are common to all the helical angles.
For the sake of brevity, the displacement patterns are further restricted
to the outer radius of the pipe and to only the axial and torsional
components of the normalized displacement vector. FIGS. 27A to 27D
illustrate the displacement patterns for the common modes T.sub.0,
T.sub.1, T.sub.2 and T.sub.3 (as labeled in FIG. 26A) at frequencies of
0.3 MHz, 0.36 MHz, 0.48 MHz, and 0.67 MHz, respectively. As stated in the
previous section, both lambtype and shear horizontal circumferential
guided waves (90.degree. helical angle) have common dispersion curves,
which also happen to be the modes that are highlighted in FIG. 26D.
Therefore, in FIGS. 27A to 27D, the displacement values for the
90.degree. helical angle are numerical aberrations as the results were
calculated using a threedimensional model (i.e., decoupled
twodimensional analysis predicts that both axial (shear horizontal) and
torsional (lambtype) displacements are independently possible). In FIG.
27A, the axial displacement seems to be predominant for the axially
propagating (0.degree. helical angle) torsional wave mode (T.sub.0). This
is also an artifact of using a threedimensional model for numerical
analysis as the decoupled analytical result predicts that the torsional
displacement should be the predominant displacement component. FIGS. 27A
to 27D, however demonstrate that the common helical guided wave modes
have predominantly torsional displacement components in general, except
for the model labeled as T.sub.0 that has predominantly an axial
displacement component.
[0127] Finite Element Simulation
[0128] Finite element simulations were performed to verify the possibility
of unfocussed beam forming. Finite element methods are based on a
separate mathematical formulation. This formulation can be found in the
manuals of the opensource software FEniCS, which was used to program the
finite element simulations for this patent. The finite element
formulation also involves time marching for which several schemes exist
in literature. For the results presented herein, the timemarching scheme
corresponds to the implicit Euler method, unless otherwise stated. The
simulations performed thus far have verified the beam steering of only
the T.sub.0 mode. From the results in FIG. 27A, the displacement pattern
for this mode is known to be predominantly axial for most of the helical
angles. Therefore, the guided wave actuation mimicking that of FIG. 17
was used. The transducer array configuration similar to FIG. 23 was used.
It may be noted that instead of a semicircular pattern a fully circular
pattern was used. The elements were arranged into a 4.times.16 grid
(i.e., the flattened array including 4 elements along each radial row and
16 such rows along the tangential direction). The element diameter was
maintained at 1/16th of an inch. The elements were tightly packed in the
radial direction. The small transducer size and spacing are beneficial so
that plate guided wave beam forming theory may be adapted to
approximately evaluate the phase delays. The frequency of excitation was
maintained at 0.35 MHz. Snapshots of the finite element simulation are
shown in FIGS. 28A and 28B for the helical angles of 45.degree. and
60.degree., respectively, relative to the pipe axis. These results
demonstrate that helical guided wave beams can be formed and steered.
These results also partially confirm the theoretical predictions
corresponding to FIG. 27A. Efforts to improve the computational speed and
to test beam forming and steering for a greater range of helical angles
is underway.
[0129] Summary of Select Disclosed Embodiments
[0130] The disclosed subject matter includes a method and a system for
unfocused and focused beam forming and steering of ultrasonic guided
waves in a pipe along helical path.
[0131] In one embodiment, a device includes an array of at least two
ultrasonic transducers elements that can excite and receive sound or
elastic waves in the pipe, or any implementation of such an array,
exemplified by macrofiber composites. The device includes an electronic
system that can control or drive the ultrasonic transducer elements in
the array. The control parameters may comprise one or more of the
following: a continuously oscillating signal amplitude, a windowed pulsed
signal comprising at least half an oscillation of any shape, signal whose
frequency content may vary with time, a prescribed range of frequencies,
varying time delays and/or amplitudes and/or number of cycles (or pulse
length) and/or frequencies. In one embodiment, the device includes an
optional array of at least one ultrasonic receiver. In another
embodiment, the device includes an electronic system that can amplify and
conditioning the signals received from each transmitting and/or receiving
sensor.
[0132] In one embodiment, a method includes evaluation and selection of
guided wave subtypes, helical paths and focal points enabled by new
method of formulating guided waves in pipes. The above parameters are
evaluated based on the above selection for electronically controlling the
waves generated in the pipe. Detection of the defects and features in the
pipe may be based on the presence or absence of anomalous signatures,
such as reflections and transmissions of ultrasound from the defects. The
features based on the amplitude distribution in time and/or frequency,
arrival time and direction of approach of such signatures are mapped.
[0133] In one embodiment, a method for inspecting the pipe wherein the
inspection includes detecting, locating and sizing flaws by processing
the reflections resulting from beam formed waves that impinge on the
flaws at multiple angles of incidence, where such reflections are
received as signals by the above mentioned system of arrays and
electronics. Further, the flaws may include a shape and/or orientation
with a minimum size determined by the period or alternately the frequency
of oscillation of the generated wave in time and space.
[0134] In one embodiment, a method for using special transducer array
elementsthat individually generate omnidirectional waveswhose
configuration is determined by the direction of oscillation relative to
the rays comprised by the propagating wave in the pipe or to the axis of
the pipe. In some examples, the oscillation is one of: oscillation along
the wall thickness of pipe using a traditional thickness mode
piezoelectric transducer or specially shaped 13 piezocomposite;
oscillation tangential and along the axis of the pipe using a circular
shape macrofiber composite with piezoelectric fibers oriented
perpendicular to the axis and the electrodes arranged along the axis;
oscillation tangential and orthogonal to the axis of the pipe using a
macrofiber composite that is circular in shape but the piezoelectric
fibers are oriented along the axis of the pipe whereas the electrodes are
oriented perpendicular to the axis; oscillation tangential but orthogonal
to the rays comprised by the wave a circular shaped macrofiber composite
where the fibers form an annular array and the electrodes are oriented
radially from the center of the annular array; oscillation tangential but
parallel to the rays in the wave using a circular shaped macrofiber
composite where the electrodes form an annular array but the
piezoelectric fibers are oriented radially from the center of the annular
array; or other transduction mechanisms, such as electromagnetic acoustic
transducers or magnetostrictive transducers.
[0135] In some embodiments, the devices disclosed herein are capable of
generating both bidirectional and unidirectional beams. In some
embodiments, the devices disclosed herein are capable of being used for
focused beam forming and steering in platelike structures. In some
embodiments, the methods disclosed herein can also be used for
postprocessing ultrasonic radar data. In some embodiments, the devices
disclosed herein can also be used for applications that require high
intensity ultrasound, such as are nonlinear ultrasonic testing,
ultrasonic deicing, ultrasonic cleaning, and processes involving
sonochemistry.
[0136] It should be noted that for purposes of this disclosure,
terminology such as "upper," "lower," "vertical," "horizontal,"
"inwardly," "outwardly," "inner," "outer," "front," "rear," etc., should
be construed as descriptive and not limiting the scope of the claimed
subject matter. Further, the use of "including," "comprising," or
"having" and variations thereof herein is meant to encompass the items
listed thereafter and equivalents thereof as well as additional items.
Unless limited otherwise, the terms "connected," "coupled," and "mounted"
and variations thereof herein are used broadly and encompass direct and
indirect connections, couplings, and mountings.
[0137] The principles, representative embodiments, and modes of operation
of the present disclosure have been described in the foregoing
description. However, aspects of the present disclosure which are
intended to be protected are not to be construed as limited to the
particular embodiments disclosed. Further, the embodiments described
herein are to be regarded as illustrative rather than restrictive. It
will be appreciated that variations and changes may be made by others,
and equivalents employed, without departing from the spirit of the
present disclosure. Accordingly, it is expressly intended that all such
variations, changes, and equivalents fall within the spirit and scope of
the present disclosure, as claimed.
* * * * *